Gauss Law Problems, Cylindrical Conductor, Linear & Surface Charge Denisty, Electric Field & Flux,  Summary and Q&A
TL;DR
Using Gauss's law, the total charge enclosed by a Gaussian cylinder can be calculated by multiplying the surface charge density, the lateral area of the cylinder, and the length of the Gaussian cylinder. The electric flux passing through the Gaussian cylinder is determined by dividing the total charge enclosed by the cylinder by the electric constant. The electric field at a distance of 1.5 meters away from the cylindrical conductor can be found by multiplying the surface charge density, the radius of the conductor, and the radius of the Gaussian cylinder, and dividing it by the electric constant times the radius of the Gaussian cylinder.
Key Insights
 🈂️ The surface charge density, lateral area, and length are used to calculate the total charge enclosed by a Gaussian cylinder in a cylindrical conductor.
 👮 Gauss's law relates the total charge enclosed by a Gaussian surface to the electric flux passing through it.
 🏑 The electric field inside a cylindrical conductor is zero, while outside it is determined by the surface charge density and the distance from the conductor.
 🈂️ The linear charge density of the cylindrical conductor is the product of the surface charge density and the circumference of the conductor.
Transcript
an infinitely long cylindrical conductor has a radius of 30 centimeters and a surface charge density of 15 micro coulombs per square meter what is the total charge enclosed by a gaussian cylinder of radius 1.5 meters and length 2 meters so let's begin by drawing a picture so we're going to have is a cylindrical conductor and then outside of that we... Read More
Questions & Answers
Q: How is the total charge enclosed by a Gaussian cylinder in the cylindrical conductor calculated?
The total charge is determined by multiplying the surface charge density, the lateral area of the cylinder, and the length of the Gaussian cylinder.
Q: What is the formula for calculating the electric flux passing through the Gaussian cylinder?
The electric flux is equal to the total charge enclosed by the cylinder divided by the electric constant.
Q: What is the formula for calculating the electric field at a distance of 1.5 meters away from the cylindrical conductor?
The electric field is found by multiplying the surface charge density, the radius of the conductor, and the radius of the Gaussian cylinder, and dividing it by the electric constant times the radius of the Gaussian cylinder.
Q: Why is the electric field inside the cylindrical conductor equal to zero?
The electric field inside any metal conductor is zero because all of the charge is distributed on the surface of the conductor.
Summary & Key Takeaways

The total charge enclosed by a Gaussian cylinder in an infinitely long cylindrical conductor can be determined by multiplying the surface charge density, the lateral area of the cylinder, and the length of the Gaussian cylinder.

The electric flux passing through the Gaussian cylinder is calculated by dividing the total charge enclosed by the cylinder by the electric constant.

The electric field at a distance of 1.5 meters away from the cylindrical conductor can be found by multiplying the surface charge density, the radius of the conductor, and the radius of the Gaussian cylinder, and dividing it by the electric constant times the radius of the Gaussian cylinder.